A group of leading Silicon Valley CEOs renewed their call on Congress to rein in government surveillance of Internet users, as a key U.S. Senate committee prepared to hear testimony Thursday on a House bill that the tech leaders say doesn’t go far enough.

“Confidence in the Internet, both in the U.S. and internationally, has been badly damaged over the last year,” the CEOs complained in an open letter to the Senate, signed by Google’s Larry Page, Facebook’s Mark Zuckerberg, Apple’s Tim Cook and the chiefs of Microsoft, Yahoo, Twitter, LinkedIn, AOL and Dropbox.

Tech companies and civil liberties groups have joined in criticizing the USA Freedom Act, which the House of Representatives passed last month with Obama administration support. The bill would end bulk collection of Americans’ phone records by the National Security Agency. But critics say it could still allow collection of “metadata” from Internet communications, such as the names of people who exchange emails.

That was “something that the administration and Congress said they intended to end,” the CEOs said in their letter. which urges the Senate to adopt stricter language. Internet companies also want the law to let them reveal more details about the volume and types of information sought by government agencies.

The Senate Intelligence Committee will hold a hearing on the bill Thursday afternoon. Committee Chairwoman Dianne Feinstein, D-Calif., has previously voiced support for the bill’s approach to ending bulk collection of phone records. While she’s also argued for protecting national security, opponents say they’re hopeful she is open to additional reforms.

The hearing comes on the anniversary of news reports about NSA phone surveillance based on leaks by former contractor Edward Snowden. A day later came the first of several reports about Internet spying programs, also based on Snowden leaks.

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